The present invention relates to an improved full-wave rectifier circuit, and more particularly to a full-wave rectifier using an operational amplifier.
A prior art full-wave rectifier uses two operational amplifiers as shown in FIG. 1. More specifically, a resistor 3, a resistor 4 and the cathode of a diode 9 are connected to an inverting input of an operational amplifier 1 whose non-inverting input is connected to a reference potential point 12. The other end of the resistor 3 is connected to an input terminal 10 and to a resistor 5; and the other end of the resistor 4 is connected to the anode of a diode 8 and to a resistor 6. The cathode of the diode 8 is connected to the output of the operational amplifier 1 and to the anode of diode 9; and the other end of the resistor 6 is connected to an inverting input of an operational amplifier 2 and to a resistor 7. The noninverting input of the operational amplifier 2 is connected to a reference potential 12'. The other end of the resistor 7 is connected to the output of the operational amplifier 2 and to an output terminal 11.
The operation of the rectifier in the prior art will now be explained. When a positive input voltage V.sub.INA is applied to the input terminal 10, the diode 8 is rendered conductive and the diode 9 is rendered non-conductive. The operational amplifier 1 operates as a feed-back amplifier having an amplification factor defined by resistors 3 and 4. If the resistances of the resistors 3 and 4 are denoted by R.sub.3 and R.sub.4, the output voltage V.sub.OUTD at the point D is given by the following equation (1), ##EQU1##
Here, the electric currents flowing through the resistors 5, 6 and 7 are denoted by I.sub.5, I.sub.6 and I.sub.7. If the operational amplifiers 1 and 2 have infinitely great input impedances and, since the potentials at the inputs B and E of the operational amplifiers 1 and 2 can be assumed to be the same as the reference potential, the electric currents I.sub.5 and I.sub.6 are given by the following equations (2) and (3), ##EQU2## where R5 and R6 denote resistances of the resistors 5 and 6.
Furthermore, the following equation (4) holds true among the electric currents I.sub.5, I.sub.6 and I.sub.7, EQU I.sub.7 =I.sub.5 +I.sub.6 ( 4)
If the equations (2) and (3) are substituted for the equation (4), the current I.sub.7 is given by the equation (5), ##EQU3##
If the equation (1) is substituted for the equation (5), the current I.sub.7 is given by the equation (6), ##EQU4##
Here, if the output voltage at the output point F of the operational amplifier 2 is denoted by V.sub.OUTF1 and the resistance of the resistor 7 by R.sub.7, the voltage V.sub.OUTF1 at the output point F is expressed by the equation (7), EQU V.sub.OUTF1 =-R.sub.7 .times.I.sub.7 ( 7)
Hence, if the equation (6) is substituted for the equation (7), there holds the following equation (8), ##EQU5##
If the following equations (9) and (10) hold, the equation (8) can be replaced by the equation (11), ##EQU6##
Therefore, when a positive input voltage V.sub.INA is applied to the input terminal 10, the same positive input voltage V.sub.INA appears on the output point F of the operational amplifier 2, i.e., appears on the output terminal 11, provided the above-mentioned resistances are set according to equations (9) and (10).
Next, when a negative input voltage V'.sub.INA =-V.sub.INA is applied to the terminal 10, the diode 8 is rendered non-conductive, and the diode 9 is rendered conductive. Consequently, the potential becomes zero at the point D, resulting in no voltage drop across the resistor 6, i.e., both terminals of the resistor 6 are held at the reference potential, and no current flows through the resistor 6.
From the equations (4) and (5), therefore, the equation (12) holds true. ##EQU7##
Therefore, the output voltage V.sub.OUTF2 at the output point F of the operational amplifier 2 is given by the equation (13), ##EQU8##
Here, if the equation (10) holds, the equation (13) is rewritten as, ##EQU9##
Therefore, when the negative input voltage V'.sub.INA (-V.sub.INA) is applied to the input terminal 10, a voltage of the same voltage level but having an inverted sign, i.e., the voltage V.sub.INA, is obtained from the output point F of the operational amplifier or from the output terminal 11.
Thus, the circuit of FIG. 1 operates as an absolute-value circuit which always produces output voltages of positive polarity upon receipt of input voltages of both positive and negative polarities. That is, when signals of sinusoidal waveform such as shown in FIG. 2(a) are input to the input terminal 10, the output terminal 11 produces signals in which the positive portions of the input sinusoidal waves are output in their original form while the negative portions are output after they are inverted to positive portions as shown in FIG. 2(b). In other words, the circuit in the prior art operates as a full-wave rectifier. The conventional rectifier circuit shown in FIG. 1, however, requires five resistors having accurate resistances, two diodes and two operational amplifiers, i.e., two amplifier circuits, and further must satisfy the requirements of equations (9) and (10) for the five resistors. To realize a rectifying circuit, therefore, a considerable number of elements must be used, and it is necessary to maintain very high accuracy in the resistance values of the five resistors.